In this article, we explain how our inquiry worldview informs one methodological approach we have used to better understand classroom processes and change, State Space Grids (SSGs). We describe our approach to measuring a fundamental classroom process, that of teacher-student interaction, and its influence on a valued educational outcome, student engagement. Drawing from Complex Dynamic Systems theory, we illustrate the affordances of SSGs to study stability and change in teachers' observed instructional practices in relation to students' observed engagement. Examples from observed interaction over 3 years in two classrooms show that SSGs enabled us to analyze how and why particular teacher-student "systems" developed, producing optimal and non-optimal patterns for student engagement. Conclusions involve the benefits of SSGs for our research questions and research in educational psychology.